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Battery state-of-charge (SOC) estimation is essential for a mobile robot, such as inspection of power transmission lines. It is often estimated using a Kalman filter (KF) under the assumption that the statistical properties of the system and measurement errors are known. Otherwise, the SOC estimation error may be large or even divergent. In this paper, without the requirement of the known statistical properties, a SOC estimation method is proposed using an H∞ observer, which can still guarantee the SOC estimation accuracy in the worst statistical error case. Under the conditions of different currents and temperatures, the effectiveness of the proposed method is verified in the laboratory and field environments. With the comparison of the proposed method and the KF-based one, the experimental results show that the proposed method can still provide accurate SOC estimation when there exist inexact or unknown statistical properties of the errors. The proposed method has been applied successfully to the robot for inspecting the running 500-kV extra high voltage power transmission lines.